Why should one expect eq:srequals2ew to be true? An intuitive proof, also discussed in Ref. [1]}, is that \(\mathinner {|{\sqrt{\rho _{AB}}}\rangle }\)  is dual to two copies of the original entanglement wedge, glued along the RT surface as depicted in fig:EW. The entropy \(S_R(A:B)\)  then equals \(2 EW(A:B)\)  by the RT formula and symmetry.
